On exclusion type inhomogeneous interacting particle systems
نویسنده
چکیده
For a large class of inhomogeneous interacting particle systems (IPS) on a lattice we develop a rigorous method for mapping them onto homogeneous IPS. Our novel approach provides a direct way of obtaining the statistical properties of such inhomogeneous systems by studying the far simpler homogeneous systems. In the cases when the latter can be solved exactly our method yields an exact solution for the statistical properties of an inhomogeneous IPS. This approach is illustrated by studies of three of IPS, namely those with particles of different sizes, or with varying (between particles) maximal velocities, or accelerations.
منابع مشابه
Spectral gap estimates for interacting particle systems via a Bakry & Emery – type approach
We develop a general technique, based on the Bakry–Emery approach, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of the diffusive scaling of the spectral gap of the Kawasaki model at high temperature. Similar results are derived for Kawasaki-type dynamics in the lattice wi...
متن کاملProperties of Fractional Exclusion Statistics in Interacting Particle Systems
We show that fractional exclusion statistics is manifested in general in interacting systems and we discuss the conjecture recently introduced (J. Phys. A: Math. Theor. 40, F1013, 2007), according to which if in a thermodynamic system the mutual exclusion statistics parameters are not zero, then they have to be proportional to the dimension of the Hilbert space on which they act. By using simpl...
متن کاملHeat Kernel Upper Bounds for Interacting Particle Systems
We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent interest. We also show off-diagonal estimates of Carne-Varopoulos type. MSC 2010: 82C22, 35B65, 60K35.
متن کاملAdiabatic-nonadiabatic transition in warm long-range interacting systems: the transport of intense inhomogeneous beams.
We investigate the role of the temperature in the onset of singularities and the consequent breakdown in a macroscopic fluid model for long-range interacting systems. In particular, we consider an adiabatic fluid description for the transport of intense inhomogeneous charged particle beams. We find that there exists a critical temperature below which the fluid model always develops a singularit...
متن کاملInteracting Particle Systems
3 4 CONTENTS Preface Interacting particle systems, in the sense we will be using the word in these lecture notes, are countable systems of locally interacting Markov processes. Each interacting particle system is define on a lattice: a countable set with (usually) some concept of distance defined on it; the canonical choice is the d-dimensional integer lattice Z d. On each point in this lattice...
متن کامل